Selective imaging among three or more chemical species

ABSTRACT

The harmonic relationship of certain chemical species is exploited to produce an MRI image of a single chemical species in the presence of at least two other chemical species with the acquisition of as few as two NMR images. If the chemical shift frequencies at a particular polarizing field strength can be approximated as the ratio of two odd integers, an evolution time can be chosen for the images acquired to cancel the contributions of two of the species in one image with a corresponding contribution in the other image. A image of the uncanceled species or of the cancelled species alone may be generated. A third image may be used to correct for inhomogeneities in the polarizing B 0  field.

FIELD OF THE INVENTION

This invention relates to nuclear magnetic resonance (NMR) imagingmethods and apparatus and more particularly to a method of providing animage of a particular chemical species in the environment of two otherchemical species.

BACKGROUND OF THE INVENTION

Breast augmentation or reconstructive surgery may employ implantscontaining silicone. The silicone used in breast prostheses is composedof poly-dimethylsiloxane with varying degrees of polymerization. DowCorning's implants are approximately 40% polymerized.

Rupture and leakage of the membrane containing the silicone is a knowncomplication of these procedures. The prevalence of complications is notknown because patients may be asymptomatic, however, in light ofanecdotal reports of a possible link between silicone leakage andsystemic autoimmune disease, is important to develop a sensitivenoninvasive method to detect leaks.

The leak or rupture may occur anywhere over the surface of an implantand therefore the use of three-dimensional medical imaging techniques isdesirable. Such imaging would, in theory, allow careful scrutiny of theentire surface of the implant and the detection of even small pockets ofmigrating silicone near that surface.

NMR imaging ("MRI") is one technique capable of the necessary threedimensional imaging. A uniform magnetic field B₀ is applied to an imagedobject along the z-axis of a Cartesian coordinate system, the origin ofwhich is within the imaged object. The effect of the magnetic field B₀is to align the object's nuclear spins along the z-axis. In response toradio frequency (RF) pulses of the proper frequency oriented within thex-y plane, the nuclei resonate at their Larmor frequencies according tothe following equation:

    ω=γB.sub.0                                     ( 1)

where ω is the Larmor frequency, and γ is the gyromagnetic ratio whichis a property of the particular nucleus. Water, because of its relevanceabundance in biological tissue and the properties of its proton nuclei,is of principle concern in most imaging. The value of the gyromagneticratio γ for protons in water is 4.26 kHz/Gauss and therefore in a 1.5Tesla polarizing magnetic field B₀, the resonant or Larmor frequency ofwater protons is approximately 63.9 MHz. The other primary constituentof biological tissue is fat. Larmor frequency of protons in fat isapproximately 203 Hertz higher than that of the protons in water in a1.5 Tesla polarizing magnetic field B₀.

In the well known slice selective MRI sequence, a z-axis magnetic fieldgradient, G_(z) is applied at the time of an RF pulse so that only thenuclei in a slice through an object in the x-y plane are excited intoresonance. The coherence between the nuclei decays as characterized bytwo relaxation times T₁ and T₂. After excitation of the nuclei, magneticfield gradients are applied along the x and y axes and an NMR signal isacquired. The gradient field along the x-axis, G_(x), causes the nucleito precess at different resonant frequencies depending on their positionalong the x-axis; that is, G_(x) spatially encodes the precessing nucleiby frequency. Similarly, the y-axis gradient, G_(y), encodes y positioninto the change of magnetization or NMR signal phase as a function ofG_(y) gradient amplitude. This process is typically referred to as phaseencoding.

From this data set, an image may be derived according to well knownreconstruction techniques. The image comprises an array of complex pixelvalues having magnitude and phase. Typically the magnitudes of thepixels are mapped to a gray scale to form the visual image.

In a 1.5 Telsa B₀ field the Larmor frequency of the silicone protons isapproximately 102 Hertz higher than the protons of fat and 305 Hertzhigher than the protons of water. The difference between the Larmorfrequencies of different isotopes or species of the same nucleus, viz.,protons, is termed chemical shift, reflecting the different atomicenvironments of the species.

As noted above, the silicone used in such breast implants is composed ofpoly-dimethylsiloxane with varying degrees of polymerization. Theprimary NMR signal is from magnetically equivalent protons on the methylgroups which rapidly rotate about the Si-C bond axis. The singleresonance has fairly long T₁ and T₂ relaxation times. Other protons inthe silicone gel are present in very low concentrations (e.g., residualD4 monomers) or have very short T₂ relaxation times (e.g., cross-links)and are not detectable by MR imaging.

Critical to imaging a breast prosthesis is the ability to isolate thesilicone signal from the water and fat signals comprising the majorityof the breast tissue. In theory, because the silicone protons have adiscrete and separate resonance from fat or water protons, the signalfrom the silicone should be capable of isolation from that of fat andwater. Nevertheless, the small difference between the frequency ofresonance of the fat and silicone protons at even high field strengthsof 1.5 Tesla restricts the use of selective excitation techniques, orsaturation of the silicone resonance, to cases of extremely good B₀field homogeneity.

Three Point Dixon

As described above, an NMR signal vector is composed of a magnitude andan angle. Only the magnitude, which represents the density of detectedspins, is usually displayed in an image. The angle provides the relativephase of the detected spins.

An NMR image can be decomposed into several chemical shift components bycombining two NMR images S₀ and S.sub.π in which the spins of the twospecies are in phase and out of phase by π radians respectively ("Dixontechnique"). For example, images of fat or water alone may beconstructed by adding or subtracting the complex numbers representingeach pixel of these two images S₀ and S.sub.π, on a pixel by pixelbasis, to cancel the unwanted species. The phase shift between fat andwater components of the images may be controlled by timing the RF pulseof the NMR sequence so that the signal from the fat image evolves in itsphase with respect to the water signal by the proper angle of exactly πbefore the NMR signal is acquired.

The phase evolution is caused by the chemical shift between the twospecies and is strongly dependent on the strength of the polarizingmagnetic field B₀. Variations or inhomogeneities of B₀ caused both byimperfect shimming of the polarizing magnet or the effect of the imagedobject on the magnetic field can change the degree of phase evolutioncausing the decomposed images to contain admixtures of the two species.The accuracy of such chemical shift "Dixon" techniques is thereforeoften unreliable.

The reliability of the Dixon technique can be improved by adding a thirdimage, S₂π, to the three point Dixon technique. The third image isselected to have both chemical species in-phase after an additionalevolution time from the original in-phase image. The variation in phasebetween the first and last image is used to deduce the effects caused bymagnetic field inhomogeneity. Thus, this third image can be used todetect and correct for the effect of B₀ magnetic field inhomogeneities.

This process of deducing the effects of inhomogeneities in the magneticfield from the third image requires determination of a "switch function"which can be either plus or minus one. This switch is a function of the"wrapping" around of trigonometric functions at large angles. The threepoint Dixon technique and a method for determining the switch functionis described in detail in U.S. Pat. No. 5,144,235 to Glover et al.assigned to the same assignee of the present application and herebyincorporated by reference.

SUMMARY OF THE INVENTION

The present invention recognizes that the three point Dixon techniquecan be extended, in certain situations, to distinguish one chemicalspecies from not only a second species, as has been done with previousthree point Dixon techniques, but from a second and third chemicalspecies. Because most body tissue include both water and fat, theinvention provides an important ability to image a foreign, non-fat,non-water, chemical species, such as silicone, introduced into the body.

The use of phase differences to separate one material from two (asopposed to one) other materials is problematic. With two materials, itis a simple matter to adjust the relative phase of the materials in eachimage to the proper relationship, by waiting an evolution time based ontheir chemical shift difference. But with three species, a singleevolution time will generally only produce the desired phase shiftbetween two of the species, the phase shift between the third and theother two will be an undesired arbitrary amount, the function of adifferent chemical shift. Thus, one might expect it to be extremelydifficult if not impossible to produce the desired phase shifts betweenthree chemical species with the three point Dixon technique.

To the contrary, the present invention recognizes that an importantclass of chemical species can be separated from water and fat by threepoint Dixon techniques and discloses the technique for determining theproper evolution time for such separation.

Specifically, to produce an image of a first chemical species in thepresence of a second and third chemical species, the second specieshaving a chemical shift frequency difference of Δω₁,2 with respect tothe first chemical species and the third chemical species having achemical shift frequency difference of Δω₁,3 with respect to the firstchemical species, both in the presence of a polarizing magnetic fieldB₀, the following steps are taken. First, frequencies ω_(a) and ω_(b)are identified approximating frequencies Δω₁,2 and Δω₁,3 and so that theratio ω_(a) :ω_(b) equals a ratio of two odd integers, i_(a) and i_(b).From these frequencies, an evolution time τ is selected to equal##EQU1## . As few as two NMR images are then acquired, the first havingan evolution time of kτ, where k is an even integer including zero, inwhich the relative phase of the three species is equal, and is secondimage having an evolution time of lτ where l is an odd integer. Theseimages are combined to produce a chemical species image with reducedcontribution from the second and third species.

For example, in the case of isolating an image of silicone in thepresence of fat and water in a polarizing field B₀ of 1.5 Tesla, Δω₁,2=102 H₃ and Δω₁,3 =305 H₃. Values ω_(a) =100 and ω_(b) =300 may beselected having a ratio of 1 to 3. The evolution time is i_(a) =1divided by (4 times 100), i.e. 1/400.

It is thus one object of the invention to provide a simple technique forisolating one chemical species from an environment containing two otherchemical species. The use of as few as two images eliminates the needfor additional NMR acquisitions thus shortening the examination time,and in some instances reducing the noise of the acquired signals. Athird image may be employed for the reduction of the effects ofinhomogeneities in the polarizing magnetic field B₀.

For the isolation of chemical species with short T₂ relaxation times,the cancellation of the unwanted species is accomplished by combinationof the second and third acquired images. For the isolation of chemicalspecies with long T₂ relaxation times, the cancellation of the unwantedspecies is accomplished by combination of the first, second and thirdacquired images.

It is thus another object of the invention to improve the cancellationof the unwanted species from an NMR image by selection among the threeacquired images depending on the characteristics of the species beingisolated. As will be explained in detail below, the use of three imagescan introduce errors in the cancellation process when the T₂ relaxationtime is short, such errors being lessened by the use of only the latertwo images.

Other objects and advantages besides those discussed above shall beapparent to those experienced in the art from the description of apreferred embodiment of the invention which follows. In thisdescription, reference is made to the accompanying drawings, which forma part hereof, and which illustrate one example of the invention. Suchexample, however, is not exhaustive of the various alternative forms ofthe invention, and therefore reference is made to the claims whichfollow the description for determining the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of an NMR system;

FIG. 2(a) is a graphic representation of a simplified gradient recalledecho sequence such as may be produced on the NMR system of FIG. 1 and asis suitable for use with the present invention,

FIG. 2(b) is a graphical representation similar to FIG. 2(a) but of aspin echo NMR pulse sequence also suitable for use with the presentinvention;

FIG. 3 is a perspective view of the net magnetic moment of three speciesof protons: silicone, fat and water, after excitation by the RF pulse,precess in the x-y plane showing the spread of the component phases foreach species caused by chemical shift,

FIG. 4 is a chart showing the component phases of the protons in twoimages used in the two point Dixon technique and in particular therelative orientations of two proton species (fat and water) at the timeof signal acquisition, as depicted in a rotating frame of referencerelative to the water protons;

FIG. 5 is a table similar to that of FIG. 4 but with three imagesshowing the relative orientation of the spins of fat and water atdifferent evolution times in the presence of a vector indicating phaseoffset caused by inhomogeneities in the B₀ field which may be eliminatedthrough the three point Dixon method. The rotating reference frame isrelative to the water protons without B₀ inhomogeneities;

FIG. 6 is a diagrammatic spectrum of resonance frequency at 1.5 Teslafor a three species system of water, fat and silicone such as may beimaged in the present invention;

FIG. 7 is a chart similar to FIGS. 4 and 5 showing the relativeorientations of the spin vectors of water, fat and silicone for threeimages having three evolution times in a rotating frame of referencerelative to the silicone protons;

FIG. 8 is a plot of percentage silicone, fat, and water in asilicone-only image, processed according to the present invention toshow only silicone, as a function of the assumed chemical shift betweenfat and silicone on which the evolution time τ is based;

FIG. 9(a) is a plot of phase shift (Δφ) versus evolution time for thesystem of FIGS. 6 and 7 showing convergence of the phase angle of fatand water at 0, -π or +π for different evolution times;

FIG. 9(b) is a plot of absolute phase difference between the fat,silicone and water protons versus evolution time; and

FIGS. 10(a) and 10(b) are graphs of pixel magnitudes for three imagesused in the present invention showing error resulting from linearinterpolation with species of different T₂ relaxation times.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, an NMR imaging system of a type suitable for thepractice of the invention includes a computer 10 which controls gradientcoil power amplifiers 14 through a pulse control module 12. The pulsecontrol module 12 and the gradient amplifiers 14 together produce theproper gradient waveforms G_(x), G_(y), and G_(z), as will be describedbelow, for a gradient echo pulse sequence. The gradient waveforms areconnected to gradient coils 16 which are positioned around the bore ofthe polarizing magnet 34 so that gradients G_(x), G_(y), and G_(z) areimpressed along their respective axes on the polarizing magnetic fieldB₀ from magnet 34. The magnet 34 homogeneity can be adjusted by means ofshimming coils 40 and a power supply 38.

The pulse control module 12 also controls a radio frequency synthesizer18 which is part of an RF transceiver system, portions of which areenclosed by dashed line block 36. The pulse control module 12 alsocontrols a RF modulator 20 which modulates the output of the radiofrequency synthesizer 18. The resultant RF signals, amplified by poweramplifier 22 and applied to RF coil 26 through transmit/receive switch24, are used to excite the nuclear spins of the imaged object (notshown).

The NMR signals from the excited nuclei of the imaged object are pickedup by the RF coil 26 and presented to preamplifier 28 throughtransmit/receive switch 24, to be amplified and then demodulated by aquadrature phase detector 30. The detected signals are digitized by anhigh speed A/D converter 32 and applied to computer 10 for processing toproduce NMR images of the object.

Referring to FIG. 2(a), a gradient recalled echo sequence begins with atransmission of a narrow bandwidth radio frequency (RF) pulse 50. Theenergy and phase of the initial RF pulse 50 may be controlled such thatat its termination, the magnetic moments of the individual nuclei of theimaged object are precessing about the z-axis within the x-y plane showngenerally in FIG. 3. A pulse of such energy and duration is termed a 90°RF pulse.

The result of the combination of RF pulse 50 and a z-axis gradient pulseG_(z) is that the nuclear spins of a narrow slice in the imaged objectalong an x-y plane are excited into resonance. Only those spins with aLarmor frequency, under the combined field G_(z) and B₀, equal to thefrequencies contained within the bandwidth of the RF pulse 50 will beexcited. Hence, the position of the slice may be controlled by thegradient G_(z) offset or the RF frequency.

After the RF pulse 50, the precessing spins begin to dephase accordingto their chemical shifts which cause the spins of certain chemicalspecies to precess faster than others. At a time T after the RF pulse50, an NMR signal 59 is acquired during the application of a x-axisgradient G_(x). The G_(x) gradient signal produces a gradient recalledecho as is understood in the art.

The shape of the G_(x) pulse is such that the water, fat and siliconeproton spins are aligned at time T having been brought into alignment bythe portion of the G_(x) gradient prior to time T. After time T, thesilicone, fat and water spins begin to dephase.

A second acquisition of signal may occur at an evolution time τ afterthe first acquisition 59' where the silicone, fat and water spins are nolonger in alignment. The degree of phase difference between the spinswill be a function of the time τ and the magnetic field strength.Similarly, with different evolution times, other signals may beacquired.

The above sequences are repeated with different gradients G_(y) 57 as isunderstood in the art to acquire multiple NMR signals 59 which may bereconstructed according to conventional reconstruction techniques.

Referring to FIG. 2(b), a spin echo pulse sequence also begins with thetransmission of a narrow bandwidth radio frequency (RF) pulse 50. Again,energy and the phase of this initial RF pulse 50 are controlled suchthat at its termination, the magnetic moments of the individual nucleiare precessing around the z axis within the x-y plane.

After the 90 RF pulse 50, the precessing spins begin to dephaseaccording to their chemical shifts which cause the spins of certainchemical species to precess faster than others. At time TE/2 after theapplication of 90 RF pulse 50, a 180 RF pulse 54 may be applied whichhas the effect of rephasing the spins to produce a spin echo 56 at timeTE after the 90 RF 50. This spin echo signal 56 is acquired during aread out gradient 53.

As is understood in the art, a dephaser pulse 52 is applied after the 90RF pulse but before the read out gradient to center spin echo within theread out gradient.

With the 180 pulse 54 centered at time TE/2 the fat, water and siliconeproton spins will be completely rephased and hence have no phase shiftwith respect to each other at the time of the spin echo 56. The time ofthe 180 pulse 54, however, may be shifted forward or back by time τ fromthe time TE/2. In this case, the fat, water and silicone proton spinswill not be in phase but will be shifted with respect to each other.

The above sequences are repeated with different G_(y) gradient pulses57, as is understood in the art, to acquire an NMR data set from which atomographic images S₀, S.sub.π and S₂π of the imaged object may bereconstructed according to conventional reconstruction techniques usingthe Fourier transform.

Three tomographic images: S₀, S.sub.π and S₂π of the imaged object areacquired as will now be described. Referring to FIG. 4, in the prior arttwo-point Dixon technique, an evolution time τ was chosen so that thetwo images obtained have the phase differences between the fat and waterspins (58 and 55 in FIG. 3) of 0 and π in images S₀ and S_(x)πrespectively. Adding and subtracting these images S₀ and S.sub.πprovides separate fat and water images.

In the ideal case, the frequency of the RF modulator 20 and phasedetector 30 are adjusted to match the Larmor frequency of the water. Ifthe polarizing magnetic B₀ is uniform, this resonance condition isachieved throughout the entire subject. Similarly, the out-of-phasecondition (π radians) for the fat component is achieved for alllocations in the subject under homogeneous field conditions as shown inFIG. 4. In this case, the two point decomposition into the separateimages is ideal in that fat is completely suppressed in the water image,and vice versa. When the polarizing field is inhomogeneous as shown inFIG. 5, however, there are locations in the subject for which the wateris not on resonance. In this case, the accuracy of the decompositionbreaks down and the water and fat images contain admixtures of the twospecies. This derives from additional phase shifts of the NMR signalcaused by the B_(o) inhomogeneities. The degree to which the offresonance condition holds is, in general, not known. The accuracy ofsuch chemical shift "Dixon" techniques is therefore often unreliable.

Field inhomogeneities may result from improper adjustment or shimming ofthe polarizing magnetic field B₀, but are more typically the result of"demagnetization" effects caused by the variations in magneticsusceptibility of the imaged tissue, such as between soft tissue andair, or bone and soft tissue, which locally distort the polarizingmagnetic field B₀. These demagnetization effects may be of short spatialextent but of high magnitude, and therefore may not be removed byconventional linear or higher order shimming techniques.

The influence of demagnetization may be accommodated, however, by animaging technique that uses three images S₀, S.sub.π, and S₂π, with thephase evolution times adjusted so that the fat and water components ofthe images are in phase, out of phase by π, and in-phase by 2πrespectively. The complex pixels in each of the three images afterconventional reconstruction may be represented as follows:

    S.sub.0 =(ρ1+ρ2)e.sup.iφ0                      (2)

    S.sub.π =(ρ1-ρ2)e.sup.i(φ+φ0)           (3)

    S.sub.2π =(ρ1+ρ2)e.sup.i(2φ+φ0)         (4)

where ρ₁ is the (real) relaxation weighted spin density and hence theamplitude of the pixel contributed by the water component, ρ₂ is the(real) relaxation weighted spin density or amplitude of the pixelcontributed by the fat component, and φ₀ is the phase shift common toall acquisitions that is caused by RF heterogeneity due to penetrationeffects, phase shifts between the RF transmitter and receiver, and othersystematic components. These effects are independent of chemical shiftbut dependent on spatial location. In image S.sub.π, the amplitudes ρ1and ρ2 are subtracted because of the π phase shift between the fat andwater components as previously described The phase shift φ is caused bythe unknown resonance offset that results from B₀ heterogeneity.

The phase offset φ₀ may be eliminated from equations (2)-(4) from S₀,since the ρ_(i) values are real quantities, by determining its argumentφ₀. The argument φ₀ may then be eliminated from the equations (2)-(4)yielding:

    S'.sub.0 =S.sub.0 e.sup.-iφ0 =(ρ1+ρ2)          (2')

    S'.sub.π =S.sub.π e.sup.-iφ0 =(ρ1+ρ2)e.sup.i(φ)(3')

    S'.sub.2π =S.sub.π e.sup.-iφ0 =(ρ1+ρ2)e.sup.i(2φ)(4')

The values of p₁ and p₂ may be determined from the measured values ofS'₀, S'.sub.π and S'₂π according to equations ##EQU2## where s is a"switch function" which may be either +1 or -1 thus determining the signof the average. The latter equations (5') and (6') provide arithmeticrather than geometric averaging of S'₀ and S'₂π.

The choice of the sign of the averages is difficult because thedemagnetization effects may cause abrupt changes in the local polarizingmagnetic field B₀ which cause the switch function to change in valuefrom pixel to pixel. A method of determining the value of the switchfunction is provided in U.S. Pat. No. 5,144,235 entitled: MethodDecomposing NMR Images by Chemical Species, assigned to the sameassignee as the present invention and hereby incorporated by reference.

Referring to FIG. 5, the three point Dixon method may be compared to thetwo point Dixon method of FIG. 4. Here three images S₀, S.sub.π and S₂πare obtained with relative phase shifts between the fat and water of 0,π and 2π. The phase shift caused by B₀ inhomogeneities is shown for eachof the evolution times and simply adds to the phase shift caused by thechemical shift of the fat and water components. The third image S₂π canbe used to deduce this B₀ effect which may then be subtracted out of theS₀ or S.sub.π images in principle to produce a decomposition as desired.

Referring now to FIG. 6, a spectrum encountered with a breast prosthesishaving voxels of water, fat and silicone exhibits three resonant peaks.The water and fat peaks common to most in vivo imaging are separated by203 Hertz in a 1.5 Tesla field. The fat resonance contains severalprotons species: methyl CH₃, methylene CH₂, and methyne CH, withslightly different resonant frequencies. In addition, adjacent protonsare coupled via indirect dipolar couplings (J-couplings) to each other.These two effects cause the fat resonance to have a natural line widthof about 40 Hertz. Only one resonance is observed for silicone, themethyl protons resonate at 305 Hertz above water.

Three point Dixon technique of FIG. 5 will not work for arbitrary threespecies systems. For Dixon three point decomposition, each of thespecies must be substantially either in-phase or out of phase with thespecies being isolated. This allows the images to be added or subtractedto eliminate contributions from the undesired species. Although any twoof the species may be placed in an arbitrary phase relationship by theappropriate evolution time τ, in general, the third species will have aphase relationship unsuitable for decomposition.

Nevertheless, as illustrated in FIG. 6, the ratio of the chemical shiftfrequencies of silicone, fat and water are such that three pointdecomposition may be undertaken. Referring also to FIG. 7, and assumingthat the B₀ field is perfectly homogenous, three images S₀, S.sub.π andS₂π may be obtained by allowing the fat component to have a phase shiftof π and 2π with respect to the silicone, as shown in FIG. 7 with thewater component having a phase shift of 3π and 6π with respect to thesilicone, which is essentially equivalent to π and 2π phase differenceof fat. Generally then, these images may be added to produce asilicone-only image (ρ₃).

More specifically, the acquisitions taken produce the following images:

    S.sub.0 =(ρ.sub.1 +ρ.sub.2 +ρ.sub.3)           (7)

    S.sub.π =(ρ.sub.1 e.sup.i(θ=3π) +ρ.sub.2 e.sup.i(θ=π) +ρ.sub.3)e.sup.i(φ+φ)   (8)

    S.sub.2π =(ρ.sub.1 e.sup.i(θ=6π) +ρ.sub.2 e.sup.i(θ=2π) +ρ.sub.3)e.sup.i(2φ+φ.sub.0)(9)

Where π1, π2 and π3 are the amplitude of the water, fat and siliconecomponents respectively and φ₀ is a phase offset resulting from RFpenetration and other systematic phase shifts. φ is the phase shiftchange caused by magnetic field homogeneity and magnetic susceptibilityduring the Dixon delay time τ.

Subtracting the offset phase φ₀ from each of the images produces:

    S'.sub.0 =(ρ.sub.1 +ρ.sub.2+ρ3)                (10)

    S'.sub.90 =(-ρ.sub.1 -ρ.sub.2 +ρ3)e.sup.iφ (11)

    S'.sub.2π =(ρ.sub.1 +ρ.sub.2 +ρ3)e.sup.2iφ(12)

The phase terms of S'₂π and S'.sub.π are subtracted, fit and thenunwrapped producing a combination magnetic susceptibility and B₀ fieldinhomogeneity map φ'. The corrected phase difference map is used todetermine a switch function s as will be described and subsequently tocorrect the magnitude images.

    S".sub.0 =S'.sub.0 =(ρ.sub.1 +ρ.sub.2 +ρ.sub.3)(13)

    S".sub.90 =S'.sub.90 'πe.sup.-iφ =(-ρ.sub.1 -ρ.sub.2 +ρ.sub.3)                                             (14)

    S".sub.2π =S'.sub.2π e.sup.-2iφ =(ρ.sub.1 +ρ.sub.2 +ρ.sub.3)                                             (15)

and then to compute the pure silicone (ρ3) and complimentary water-fatimages (ρ₁ +ρ₂). ##EQU3##

EXAMPLE I

Referring to FIG. 8, an in vivo measurement of two volunteers was madeand the percent total water, fat and silicone signal in the imagesprocessed per equation (16) was plotted against the frequency differencebetween silicone and fat assumed in the calculation of τ. The RFtransmitter was centered on the silicone methyl proton resonance andscan parameters were TR=100 milliseconds, TE=25 milliseconds, FOV 16 cm,slice thickness 4 millimeters, matrix 128×256, one excitation. Theoptimum silicone fat frequency difference was found at the minimumpercentage fat in the silicone only image. This appears at about 102Hertz.

Referring now to FIG. 9(a) and (b), the relative phase of the fat spins58 and water spins 55 with respect to the silicone spins 51 and theabsolute phase differences are plotted against evolution time τ.Although a given τ affects the phase of both fat and watersimultaneously, it will be noted that because of the particular ratio ofchemical shift frequencies of fat and water with respect to silicone,that the phases of both fat and water converge at |π| at given evolutiontime τ. While this will not be true for all possible three speciessystems, a large number of systems will meet the requirements necessaryfor successful decomposition.

The requirements for such decomposition may be established as follows.Referring still to FIG. 9, for an arbitrary three species system, therelative chemical shift of the second species with respect to the firstspecies is Δω₁,2 and the relative chemical shift frequency of the thirdspecies with respect to the first species is Δω₁,3. The first species isthe species of which an isolated image will be constructed. A phaseshift between the first and second chemical species of π (or any oddmultiple of π) will occur at evolution times: ##EQU4## where n is anonnegative integer. Likewise for the third chemical species, a phasedifference of magnitude π will occur at evolution times ##EQU5##

For both the second and third chemical species to have phase shift withrespect to the first chemical species of π, it is required only for somem and n: ##EQU6##

By inspection then, the requirement is simply that the rate of thechemical shift of the second and third species be that of a ratio of oddintegers. Thus ratios of 1/1, 1/3, 3/5 etc. will allow the present threepoint technique to separate one distinct chemical species from twoothers.

Clearly, in situations where the chemical shift is not exactly a ratioof odd integers but may be approximated as such, chemical speciesisolation may still be performed with some minor degradation in theseparation. For example, the chemical shift frequencies of water and fatwith respect to silicone are in fact a fraction ##EQU7## and onlyapproximately 1/3. Nevertheless, adequate images may be obtainedassuming a 1/3 ratio. Thus frequencies Δω₁,2 and Δω₁,3 are approximatedby frequencies ω_(a) and ω_(b) having the desired odd integer ratio.

Then, τ in general, from equation (18), will be ##EQU8## where i_(a)=(2n+1) where n satisfies equation (21). Alternatively, from equation(19) τ may be where i_(b) =(2m+1) where m satisfies equation (21).Preferably, i_(a) and/or i_(b) will be the smallest possible integerssatisfying equation (21). Likewise, the image S₀ may be taken at evenmultiples of τ and not just at zero evolution time.

Referring again to FIG. 7 and equations (5) and (6), a switch function smust be determined. In general, the switch function depends on thepresence of variations in the polarizing magnetic field B₀ and may bedetermined by the information contained in the three acquired images.The process of determining the switch function s is described in detailin U.S. Pat. No. 5,144,235 to Glover et al. issued September 1, 1992assigned to the assignee of the present invention hereby incorporated byreference. Generally, as indicated in the discussion associated withFIG. 5, the phase offset of the third image S₂π is used to deduceinhomogeneity effect.

Referring to FIG. 10(a), depending on the chemical species being imaged,the NMR signal, as characterized by the relaxation times T₁ and T₂ ofthe second and third species, will become progressively weaker forincreasingly long evolution times τ. For chemical species where the T₂decay is quite rapid, the calculations of equations 5 and 6, and 16 and17 will produce considerable error owing to the effective linearinterpolation accomplished by the term ##EQU9## which averages the S"₀,S"₂π images. For any two pixels having magnitudes 100 and 102 of the S"₀and S"₂π images respectively, the linear interpolation for a rapidlydecaying signal will produce a magnitude 104 greater than the value 106of the image S"₂π which must be subtracted from the value 104 to cancelthe contributions of the unwanted species. This difference between 104and 106 will cause incomplete cancellation of the unwanted species inthe image. Preferably, therefore, in this situation, the images arecombined according to a new set of equations as follows:

    ρ.sub.3 =(S".sub.2π +sS".sub.90 )/2                 (22)

    ρ.sub.1 +ρ.sub.2 =(S".sub.2π -sS".sub.π)/2   (23)

Equations (22) and (23) take advantage of the fact that point 102 is abetter approximation of point 106 than is interpolated points 104 forspecies with short T₂ relaxation times. The disadvantage to thisapproach is a loss of signal-to-noise ratio as a result of the use ofweaker signals in generating the selective image. Equations (22) and(23) may also be used for the separation of two species under similarcircumstances.

Referring to FIG. 10(b), in situations where the decay of the NMR signalis relatively long compared to the expected evolution time, theequations (16) and (17) which provide a linear interpolation, willprovide both an good estimate of the zero phase image S₀ at theevolution time of the S.sub.π images and will produce bettersignal-to-noise ratio in the resulting selective image owing to thecombination of a greater number of images and the use of the S₀ imagehaving the greatest signal-to-noise ratio.

While this invention has been described with reference to particularembodiments and examples, other modifications and variations will occurto those skilled in the art in view of the above teachings. For example,the technique is not limited to the isolation of one chemical speciesfrom two others but may be employed to isolate one chemical species fromany group of other species provided the chemical shift frequencydifferences are such that with some evolution time τ the other chemicalspecies may be made to evolve to a phase difference of π with respect tothe species to be isolated. Of course, it will be understood that theinvention is useful for the imaging of materials other than silicone andthat the frequencies provided for the imaging of silicone are a functionof the B₀ polarizing field. Other field strengths B₀ may be used byscaling these frequencies proportionally upward (and the evolution timesproportionally downward) for increases in B₀ away from the value of 1.5Tesla considered herein.

Accordingly, the present invention is not limited to the preferredembodiment described herein, but is instead defined in the followingclaims.

I claim:
 1. A method for producing an image of a first chemical speciesin the presence of a second and third chemical species, the secondspecies having a chemical shift frequency difference of Δω₁,2 withrespect to the first chemical species and the third chemical specieshaving a chemical shift frequency difference of Δω₁,3 with respect tothe first chemical species, both in the presence of a polarizingmagnetic field B₀, the method comprising the steps of:a) identifyingfrequencies ω_(a) and ω_(b) approximating frequency difference Δω₁,2 andΔω₁,3 and so that the ratio ω_(a) :ω_(b) equals a ratio of two oddintegers i_(a) and i_(b) ; b) determining an evolution time τ beingequal to ##EQU10## c) acquiring a first complex NMR image with anevolution time of kτ, where k is an even integer including zero, inwhich a relative phase of the three species is equal; d) acquiring asecond complex NMR image with an evolution time of 1τ, where 1 is an oddinteger, so that the second and third species have a phase differencemagnitude of π; and e) combining the first and second images to producea chemical species image with reduced contribution from the second andthird species.
 2. The method of claim 1 wherein i_(a) is selected as thesmallest integer satisfying the conditions of claim
 1. 3. The method ofclaim 1 wherein the first, second and third chemical species are:silicone, fat and water respectively and wherein the values of ω_(b) andω_(a) are ##EQU11## Hz and ##EQU12## .
 4. The method of claim 1including also the step of:f) acquiring a third complex NMR image withan evolution time of 2τ; and where step (e) combines the third imagewith the first and second images to produce a chemical species imagewith reduced contribution from the second and third species andcorrection for B₀ inhomogeneities.
 5. The method of claim 4 wherein thefirst, second and third images are combined to produce the chemicalspecies image ρ₃ with reduced contribution from the second and thirdspecies according to the following equation: ##EQU13## where S"₀,S".sub.π, S"₂π are the complex NMR images and s is a switch functionresolving ambiguity in the sign of the second complex NMR image;whereinchemical species with long relaxation times may be imaged.
 6. The methodof claim 4 wherein the first, second and third images are combined toproduce the chemical species image ρ₃ with reduced contribution from thesecond and third species according to the following equation: ##EQU14##where S"₀, S".sub.π, S"₂π are the first, second, and third complex NMRimages and s is a switch function resolving ambiguity in the sign of thesecond complex NMR image;wherein chemical species with long relaxationtimes may be imaged.
 7. The method of claim 4 wherein the first, secondand third images are combined to produce the chemical speciesimage ρ₃with reduced contribution from the second and third species according tothe following equation:

    ρ.sub.3 =(S".sub.2π +sS".sub.π)/ 2

where S".sub.π, S"₂π are the second and third complex NMR images and sis a switch function resolving ambiguity in the sign of the secondcomplex NMR image; wherein chemical species with a short T₂ relaxationtime may be imaged.
 8. A method for producing an image having reducedcontribution from a first chemical species in the presence of a secondand third chemical species, the second species having a chemical shiftfrequency difference of Δω₁,2 with respect to the first chemical speciesand the third chemical species having a chemical shift frequencydifference of Δω₁,3 with respect to the first chemical species, both inthe presence of a polarizing magnetic field B₀, the method comprisingthe steps of:a) identifying frequencies ω_(a) and ω_(b) approximatingfrequency differences Δω₁,2 and Δω₁,3 and so that the ratio ω_(a) :ω_(b)equals a ratio of two odd integers i_(a) and i_(b) ; b) determining anevolution time τ being equal to ##EQU15## c) acquiring a first complexNMR image with an evolution time of kτ, where k is an even integerincluding zero, in which a relative phase of the three species is equal;d) acquiring a second complex NMR image with an evolution time of lτ,where l is an odd integer, so that the second and third species have aphase difference magnitude of π; and e) combining the first and secondimages to produce a chemical species image with reduced contributionfrom the first chemical species.
 9. The method of claim 8 i_(a) isselected as the smallest integer satisfying the conditions of claim 7.10. The method of claim 8 wherein the first, second and third chemicalspecies are: silicone, fat and water respectively and wherein the valuesof ω_(b) and ω_(a) are ##EQU16## Hz and ##EQU17## .
 11. The method ofclaim 8 including also the step of:f) acquiring a third complex NMRimage with an evolution time of 2τ; and where step (e) combines thethird image with the first and second images to produce a chemicalspecies image with reduced contribution from the first chemical speciesand correction for B₀ inhomogeneities.
 12. The method of claim 11wherein the first, second and third images are combined to produce thechemical species image ρ₁ +ρ₂ with reduced contribution from the firstspecies according to the following equation: ##EQU18## where S"₀,S".sub.π, S"₂π are the first, second, and third complex NMR images, ands is a switch function resolving any ambiguity in the sign of the secondcomplex NMR image;wherein chemical species with long relaxation timesmay be imaged.
 13. The method of claim 11 wherein the first, second andthird images are combined to produce the chemical species image π₁ +π₂with reduced contribution from the first species according to thefollowing equation: ##EQU19## where S"₀, S".sub.π, S"₂π are the first,second, and third complex NMR images and s is a switch functionresolving ambiguity in the sign of the second complex NMR image;whereinchemical species with long relaxation times may be imaged.
 14. Themethod of claim 11 wherein the first, second and third images arecombined to produce the chemical species image ρ₁ +ρ₂ with reducedcontribution from the first species according to the following equation:

    ρ.sub.1 +ρ.sub.2 =(S".sub.2π -sS".sub.π)/2

where S".sub.π, S"₂π are the second and third complex NMR images s is aswitch function resolving ambiguity in the sign of the second complexNMR image; wherein chemical species with short relaxation times may beimaged.
 15. A method for examining silicone prostheses for failure, invivo, employing magnetic resonance imaging equipment using a polarizingfield of B₀, comprising the steps of:a) acquiring a first complex NMRimage of the prostheses and surrounding tissue with a pulse having anevolution time of zero in which the relative phase of protons of water,fat, and silicone are equal; b) acquiring a second complex NMR image ofthe prostheses and surrounding tissue with an evolution time τ ofsubstantially ##EQU20## and c) combining the first and second images toproduce an image of the silicone (ρ₃) of the prostheses with reducedcontribution from fat and water (ρ₁ +ρ₂).
 16. The method of claim 15including also the step of:e) acquiring a third complex NMR image withan evolution time of 2τ; and where step (c) combines the third imagewith the first and second images to produce an image of the silicone(ρ₃) of the prostheses corrected for B₀ inhomogeneities.
 17. A methodfor producing an image having reduced contribution from a first chemicalspecies in the presence of at least a second chemical species, thesecond species having a chemical shift frequency difference of Δω₁,2with respect to the first chemical species in the presence of apolarizing magnetic field B₀, the method comprising the steps of:a)acquiring a first complex NMR image with an evolution time in which arelative phase of the two species is equal; b) acquiring a secondcomplex NMR image with an evolution time of τ so that the second specieshas a phase difference magnitude of π with respect to the first species;and c) acquiring a third complex NMR image with an evolution time of 2τin which a relative phase of the two species is equal; and d) combiningthe third image with the second image to produce the chemical speciesimage ρ₃ with reduced contribution from the second species according tothe following equation:

    ρ.sub.3 =(S".sub.2π +sS".sub.π)/2

where S".sub.π, S∝₂π are the second and third complex NMR images, and sis a switch function resolving ambiguity in the sign of the secondcomplex NMR image; wherein chemical species with short relaxation timesmay be imaged.